What is Isomap and it’s principles in Machine Learning?

Dimensionality reduction is required in modern machine learning to condense high-dimensional datasets into lower-dimensional representations while retaining all information. This simplifies data presentation, increases processing efficiency, and unveils patterns or structures that were not visible in the first place. As a non-linear dimensionality reduction method, Isomap stands out. Isomap uses graph theory and classical multidimensional scaling (MDS) to find low-dimensional structures in high-dimensional data. Isomap works best on non-linear manifolds, different from PCA.

In this article, we explore Isomap in-depth, explaining its core principles, how it works, its advantages and limitations, and its practical applications in machine learning.

What is Isomap?

​A non-linear dimensionality reduction method used in data analysis and machine learning is called isomap (isometric mapping). Its purpose is to transfer data from a high-dimensional space to a lower-dimensional one while maintaining the data’s inherent geometric structure. When datasets contain data points that sit on a non-linear manifold—that is, when the relationships between the data points cannot be captured by straightforward linear projections (as with techniques like PCA)—Isomap is very helpful.

Isomap in Machine Learning

Data is not linearly distributed in many real-world applications. Non-linear structures are common in photos, sounds, and time-series data. Complex datasets are problematic for linear methods like PCA, which presume data lie on a straight line or hyperplane. Isomap and other non-linear dimensionality reduction algorithms preserve the data’s intrinsic geometry, which linear methods struggle to represent.

    Manifold learning, a non-linear dimensionality reduction technique, assumes high-dimensional data often lie on a lower-dimensional manifold. Manifolds are topological spaces that may have larger global structures than Euclidean space. Different sources of data may be regulated by hidden variables. Isomap is designed to discover lower-dimensional structures and format the data for easier interpretation.

    Core Principles of Isomap

    The graph-based technique isomap learns a low-dimensional data representation while retaining geodesic distances. Breaking down the main ideas helps:

      • Geodesic Distance: For two points in Euclidean space, the straight-line distance is the geodesic distance. The shortest path between two points on a manifold may be a curved path on the manifold. The geodesic distance is the shortest path. In high-dimensional spaces, geodesic distances are hard to compute directly.
      • Neighborhood Graph: Each data point is connected to its nearest neighbors in Isomap’s neighborhood graph to approximate geodesic distances. By determining the shortest path through this graph, the geodesic distance may be calculated from the Euclidean distances between points. The graph will connect nearby locations in high-dimensional space but not distant ones.
      • Graph-based Shortest Path: Graph-based Once the graph is formed, Isomap calculates the shortest path between all pairs of points. A graph traversal method like Dijkstra’s or Floyd-Warshall can find the shortest path between two points. These algorithms help Isomap estimate geodesic distances.
      • Multidimensional Scaling (MDS): Isomap performs classical MDS after obtaining pairwise geodesic distances. Data is represented in a lower-dimensional space using MDS to preserve point distances. Geodesic distances are used by Isomap to embed data in a lower-dimensional space using traditional MDS.

      In summary, Isomap approximates manifold geodesic distances using neighborhood graphs and graph-based shortest path techniques. Projecting the data onto a lower-dimensional space via MDS preserves these distances.

      Steps Involved in the Isomap Algorithm

      The steps of the Isomap algorithm are:

      • Neighborhood Graph Construction: Define Euclidean distance-based nearest neighbors for each data point. Build a graph with nodes representing data points and edges the nearest neighbors’ Euclidean distances. Each point is usually connected to its k-nearest neighbors or all points within a radius.
      • Compute Geodesic Distances: Use a graph-based shortest path algorithm, such as Dijkstra’s, to compute the geodesic distance between each pair of points. The geodesic distance of the manifold can be approximated by finding the shortest path between two locations on the graph.
      • Apply Multidimensional Scaling (MDS): Apply classical Multidimensional Scaling (MDS) to obtain a lower-dimensional data representation after computing the geodesic distance matrix. Place the points in a lower-dimensional space so their pairwise distances are near to geodesic distances.
      • Output the Low-dimensional Representation: The outcome is a collection of coordinates in 2D or 3D that preserves the data’s local and global structure.

      Advantages of Isomap

      In contrast to PCA, isomap has various advantages:

        • Preserves Global Structure: PCA only records linear correlations, but Isomap preserves the manifold’s global shape. Isomap preserves geodesic distances to preserve linkages between distant points in high-dimensional space during low-dimensional representation.
        • Non-linear Data: For non-linear data on a manifold, isomap is beneficial. In image processing, Isomap can capture the non-linear relationship between pictures of objects from different perspectives on a manifold.
        • Versatile: Image, voice, genomics, and time-series data can be used with isomap. Effective when data naturally lies on a curved, non-linear manifold rather than a flat plane.

        Disadvantages of Isomap

        The powerful Isomap approach has its drawbacks:

          • Complexity: Isomap is computationally expensive, especially for huge datasets. Large datasets demand significant computational resources to build the neighborhood graph and compute the shortest paths between all pairs of points. For huge datasets, Isomap is unsuitable since shortest path techniques take quadratic or worse time.
          • Sensitivity to Parameters: The number of neighbors utilized to generate the neighborhood graph affects Isomap’s performance. Few neighbors may not capture the manifold’s structure, while too many may over-smooth. Noise in the data might also impair algorithm performance.
          • Dependence on Local Linear Approximation: Isomap believes the manifold is locally approximated by Euclidean geometry, so each local neighborhood is flat. While this is true for many datasets, Isomap may fail if the data is substantially non-linear or has significant curvature.

          Applications of Isomap

          Isomap is used in several machine learning fields despite its limitations:

          Applications of Isomap
          Applications of Isomap
            • Image Processing: Computer vision uses isomap for face recognition, image reconstruction, and object identification. Face photos taken from different perspectives or lighting circumstances typically sit on a low-dimensional manifold, which Isomap can find.
            • Speech and Audio Processing: Isomap can minimize the dimensionality of the feature space while keeping speech patterns in speech recognition due to the non-linear nature of audio signals.
            • Genomics: Isomap analyzes non-linear gene expression data in bioinformatics. Isomap can find significant patterns like gene expression profile clusters by lowering data dimensionality.
            • Time-series Data: While keeping temporal structure, isomap has also been applied to time-series data to minimize dimensionality of trajectories.

            Conclusion

            Machine learning often uses isomap to reduce the dimensionality of complex, high-dimensional data on non-linear manifolds. Using geodesic distances to preserve the data’s fundamental geometry, Isomap can find useful low-dimensional representations that reveal its structure. Due to its computational cost and parameter sensitivity, it is not ideal for large datasets or circumstances where the local linearity assumption does not apply. Although limited, Isomap is a useful machine learning tool for computer vision, speech processing, and bioinformatics.

              What is Quantum Computing in Brief Explanation

              Quantum Computing: Quantum computing is an innovative computing model that...

              Quantum Computing History in Brief

              The search of the limits of classical computing and...

              What is a Qubit in Quantum Computing

              A quantum bit, also known as a qubit, serves...

              What is Quantum Mechanics in simple words?

              Quantum mechanics is a fundamental theory in physics that...

              What is Reversible Computing in Quantum Computing

              In quantum computing, there is a famous "law," which...

              Classical vs. Quantum Computation Models

              Classical vs. Quantum Computing 1. Information Representation and Processing Classical Computing:...

              Physical Implementations of Qubits in Quantum Computing

              Physical implementations of qubits: There are 5 Types of Qubit...

              What is Quantum Register in Quantum Computing?

              A quantum register is a collection of qubits, analogous...

              Quantum Entanglement: A Detailed Explanation

              What is Quantum Entanglement? When two or more quantum particles...

              What Is Cloud Computing? Benefits Of Cloud Computing

              Applications can be accessed online as utilities with cloud...

              Cloud Computing Planning Phases And Architecture

              Cloud Computing Planning Phase You must think about your company...

              Advantages Of Platform as a Service And Types of PaaS

              What is Platform as a Service? A cloud computing architecture...

              Advantages Of Infrastructure as a Service In Cloud Computing

              What Is IaaS? Infrastructures as a Service is sometimes referred...

              What Are The Advantages Of Software as a Service SaaS

              What is Software as a Service? SaaS is cloud-hosted application...

              What Is Identity as a Service(IDaaS)? Examples, How It Works

              What Is Identity as a Service? Like SaaS, IDaaS is...

              Define What Is Network as a Service In Cloud Computing?

              What is Network as a Service? A cloud-based concept called...

              Desktop as a Service in Cloud Computing: Benefits, Use Cases

              What is Desktop as a Service? Desktop as a Service...

              Advantages Of IDaaS Identity as a Service In Cloud Computing

              Advantages of IDaaS Reduced costs Identity as a Service(IDaaS) eliminates the...

              NaaS Network as a Service Architecture, Benefits And Pricing

              Network as a Service architecture NaaS Network as a Service...

              What is Human Learning and Its Types

              Human Learning Introduction The process by which people pick up,...

              What is Machine Learning? And It’s Basic Introduction

              What is Machine Learning? AI's Machine Learning (ML) specialization lets...

              A Comprehensive Guide to Machine Learning Types

              Machine Learning Systems are able to learn from experience and...

              What is Supervised Learning?And it’s types

              What is Supervised Learning in Machine Learning? Machine Learning relies...

              What is Unsupervised Learning?And it’s Application

              Unsupervised Learning is a machine learning technique that uses...

              What is Reinforcement Learning?And it’s Applications

              What is Reinforcement Learning? A feedback-based machine learning technique called Reinforcement...

              The Complete Life Cycle of Machine Learning

              How does a machine learning system work? The...

              A Beginner’s Guide to Semi-Supervised Learning Techniques

              Introduction to Semi-Supervised Learning Semi-supervised learning is a machine learning...

              Key Mathematics Concepts for Machine Learning Success

              What is the magic formula for machine learning? Currently, machine...

              Understanding Overfitting in Machine Learning

              Overfitting in Machine Learning In the actual world, there will...

              What is Data Science and It’s Components

              What is Data Science Data science solves difficult issues and...

              Basic Data Science and It’s Overview, Fundamentals, Ideas

              Basic Data Science Fundamental Data Science: Data science's opportunities and...

              A Comprehensive Guide to Data Science Types

              Data science Data science's rise to prominence, decision-making processes are...

              “Unlocking the Power of Data Science Algorithms”

              Understanding Core Data Science Algorithms: Data science uses statistical methodologies,...

              Data Visualization: Tools, Techniques,&Best Practices

              Data Science Data Visualization Data scientists, analysts, and decision-makers need...

              Univariate Visualization: A Guide to Analyzing Data

              Data Science Univariate Visualization Data analysis is crucial to data...

              Multivariate Visualization: A Crucial Data Science Tool

              Multivariate Visualization in Data Science: Analyzing Complex Data Data science...

              Machine Learning Algorithms for Data Science Problems

              Data Science Problem Solving with Machine Learning Algorithms Data science...

              Improving Data Science Models with k-Nearest Neighbors

              Knowing How to Interpret k-Nearest Neighbors in Data Science Machine...

              The Role of Univariate Exploration in Data Science

              Data Science Univariate Exploration Univariate exploration begins dataset analysis and...

              Popular Categories